In Propositions REF , REF , and REF  below
we suppose that the space \(L^\nu \)  is finite-dimensional. In this case we take an Auerbach
basis in \(L^\nu \) , that is a basis \(e_k^\nu = e_k; k=1,...,n_\nu \)  in that space together with a basis \(e_k^{\nu *} = e_k^*\)  in
\((L^\nu )^*\)  such that \(e^*_k(e_l)=\delta _{kl}\) , and \(\Vert e_k\Vert  = 1 = \Vert e_k^*\Vert \)  for any \(k\)  (see, e.g., [1]}). We fix a distinguished element
\(w^\nu = w:=\sum _ke_k\otimes e_k^*\in {\bf L}\otimes (L^\nu )^* .\) 
